Transparent soil model testing on ground settlement induced by parallel tunnels excavation

, Hiyi, , , Wengng

a. Key Laboratory of New Technology for Construction of Cities in Mountain Area, Ministry of Education; b.School of Civil Engineering, c.National Joint Engineering Research Center of Geohazards Prevention in the Reservoir Areas; Chongqing University, Chongqing 400045, P. R. China)

Abstract: Parallel tunnels are generally constructed in urban subways to facilitate the movement of traffic in modern cities. Common solutions for predicting settlement induced by the excavation of two parallel tunnels are based on the single tunnel case and the simplified superposition method is utilized to generate the deformation profile without considering the interaction between the two tunnels. In this study, transparent soil model tests were performed to visualize the surface and subsurface settlement induced by the excavation of two parallel tunnels in sandy ground. Several key factors influencing the interaction of the parallel tunnels, as well as the surface and subsurface settlement, were investigated, including the spacing between the two tunnels, the volume of ground loss and the depth at which the tunnels were buried. Then the relationship between volume of the ground loss and the settlement was established. It is hoped that this study can provide guidelines for the design and construction of urban parallel tunnels excavations.

Keywords:transparent soil; parallel tunnels; model test; surface settlement; subsurface settlement

1 Introduction

With the rapid development of the modern city, burying the subway tunnels has proven to be an effective way to relieve traffic pressure on the ground. Accurate estimation of ground settlement is vital to ensure safety during the tunnel excavation. To this end, many early scholars have studied both the surface and the subsurface settlement for the excavation of the single tunnel[1-4]. However, single tunnel construction is rarely encountered in practice. Instead, parallel tunnels excavated sequentially are commonly constructed in urban subways to facilitate the movement of traffic in modern cities. In comparison to monitoring the deformation in clays[1-2], the settlement caused by tunneling in granular soils (e.g., sands and gravels) are more difficult and complex when considering key factors such as the relative density, which influences the shape and magnitude of the deformation[5]. Recently, the settlement of single tunnels in sand has been studied through model testing[6]and numerical simulation[7-8]. Yet the deformation induced by sequential excavation of parallel tunnels has not been fully revealed. Therefore, it may be a research hotspot in geotechnical engineering to investigate the deformation induced by the excavations of two parallel tunnels.

Many studies based on analytical deduction have been carried out to investigate the deformation induced by tunnel excavation, but they mainly aimed at the single tunnel[9-13]. Parallel-tunneling deformation prediction generally utilizes the simplified superposition method with the assumption the deformation arising from the excavation of the 2nd tunnel is unaffected by that of the 1st tunnel. However, previous research, particularly numerical studies that can fully consider the interaction between two tunnels, have indicated that this method may not be directly applicable to estimating the parallel tunneling-induced settlement in practice, since it may underestimate the resultant settlement, which may exert a negative effect on the safety of the nearby constructions[14]. The numerical simulation of tunneling which permits calculating internal soil deformation is widely used in the last decade[14-18]. However, not only is internal soil deformation difficult to validate against the actual measurements, but the key input parameters, which can directly and significantly impact the accuracy of the results, are quite difficult to obtain. Many scholars have focused on in-situ surface settlement induced by sequential excavation of parallel tunnels in a variety of soils. Since the in-situ test is costly and time-consuming, laboratory tests are widely used in performing two-dimensional trap door tests in dry sand[19]and lining installation in a centrifuge[20-21]. However, it is challenging to obtain the inner soil deformation and the failure pattern from the conventional model tests. Moreover, the results from traditional laboratory test are inevitably affected by the boundary conditions and the embedment of the rigid sensors has an effect on instrumentation accuracy due to the arching effect[22-23]. Recently the development of data-driven and soft computing methods, Zhang et al.[24-25]and Shahrour and Zhang[26]predicted the surface settlement induced by earth pressure balance shield tunneling, estimated the lining response for twin-tunnel construction, and performed TBM tunneling optimization. However, this kind of data-based method has an obvious deficiency in revealing the deformation characteristics in tunneling constructions, where the internal physical failure mechanism is often ignored.

To visualize the interioror the full-filed deformation, an advanced modeling technique using the transparent soil is adopted in this study, which was firstly developed by Allersma[27]and utilized by many scholars worldwide[28-29], including in tunneling by Ahmed and Iskander[30-31]. And the intend of this paper is to explore the parallel-tunnel interaction and its influence on surface and subsurface settlements due to the second tunnel in sandy ground considering the spacing (S) between two tunnels, the magnitude of the volume of ground loss at the tunnel (Vl)and burial depth (HandH0).

2 Experimental design

2.1 Testing apparatus

The model testing system was adopted to monitor the settlement variation during excavation. It consisted of a computer, an optical platform, a charge coupled device (CCD) camera, a disk laser, a plexiglass model tank, and processing software for particle image velocimetry (PIV) digital images. The optical platform was ferromagnetic stainless steel and the inner core structure on the top side offered considerable anti-disturbance capacity. The high resolution of the CCD camera was 1280×960 pixels, which could record the settlement during tunnel excavation continuously operated by the control program of the computer. The disk laser was EP532-3W along with 3 W output power, 532 nm wavelength, 10°-25° light angle and less than 1 mm thickness. The multifunctional model box made of acrylic plexiglass with each surface bonded by strong glue was capable of simulating the single tunnel test, parallel tunnels test and cross tunnels test, for a total of four tunnels (three on the front and one on the side). Additionally, ribs were fixed at the bottom to restrain the deformation.

2.2 Testing materials

Fused silica sand, which has similar physical and mechanical properties to the proxy naturally graded sand, was adopted in this study to manufacture the transparent soil samples. The particles were 0.5-1.0 mm in size. The maximum dry density was 1.278 g/cm3, and the minimum was 0.907 g/cm3. The relative density was 55% and the internal friction angle was between 34° and 38°. The pore liquid was mixed with n-dodecane and the 15th mineral white oil with the mass ratio of 1:4 and its refractive index was 1.458 5. The periphery of the tunnel was isolated from the surrounding soil with a self-made film tube made of transparent and highly elastic thermoplastic polyurethane (TPU) film to prevent the pore liquid from flowing out along the tunnel model hole during the test. The drainage method was used to simulate the tunnel excavation process. One end of a rubber tube with a diameter of 50 mm was tied with a wire, and the other end was sleeved on a rubber plug with a drainage tube and tied with a rubber band to prevent potential water leakage. Before the test, the model box was cleaned, and the tunnel model, as well as the waterproof film tube, was set up.

To prepare the transparent soil, marks were made every 10 mm along the vertical direction of the model box, then the volume of 10 mm thickness of the transparent soil was calculated as the unit volume and the weight of the fused silica and the amount of drainage for the unit volume were determined. The prepared mixed oil was slowly poured into the model box and then the weighed fused silica sand was uniformly poured into the model box and the mixed oil and the silica sand were mixed together. During the configuration process, the transparent soil was slowly stirred with a glass rod to eliminate the air bubbles. Then, the stratified compaction method (each layer was 10 mm thick) was used to make it satisfy the required target density. Finally, the load 1 000 kN was exerted on the prepared transparent soil for 24 hours to ensure that the relative density was constant.

2.3 Testing process

The PIV post-processing program was used to obtain the displacement from pictures during the test[32-33]. The volume of the settlement trough was directly measured by importing the experimental results into AutoCAD software according to the displacement curve of the settlement point. The stability of the sand after excavation is poor and it is difficult to form an arch. Therefore, it can be assumed that the drainage volume is equal to the convergence value around the tunnel, indicating that the volume of soil loss is equal to the volume of drainage.

The total liquid volume isVw= 687 mL. There are totally 10 times of drainage for the simulation of incremental tunnel excavation. The drainage volume is 10 mL for each time. Prior to the test, place the model box in a suitable position, put the camera right beside the model box aiming at the center of its cross section then adjust their relative position to make the image clear. Adjust the laser intensity to ensure the figure from the transparent soil form a stable and clear bright spot. TA (Tunnel A) and TB (Tunnel B) are excavated sequentially via draining the liquid in the rubber tube and every excavation footage length is 0.5D(tunnel diameter). The laser position should be moved along the sliding rail accordingly with the excavation footage.

2.4 Key influential parameters and testing schemes

For both surface settlement and subsurface settlement, six tests, divided into two groups, were performed (shown in Table 1). Group 1 and Group 2 each consisted of three tests to investigate the effects of the volume of ground loss at tunnel (Vl), burial depth (HandH0) and tunnel spacing (S) on the twin-tunnel-induced surface and subsurface settlement. The size of the model box is plotted in Fig.1, whereF=1 600 N. Fig.2 presents the cross-section diagram of the settlement trough and parts of the related parameters.

Table 1 Model Testing Scheme(a)Testing scheme for surface settlement

(b)Testing scheme for subsurface settlement

Fig.1 Schematic diagram for model dimensions and

Fig.2 Cross-sectional diagram of the settlement trough and relevant

3 Testing result and analysis

3.1 Surface settlement

3.1.1 Surface settlement due to excavation of the 1st tunnel

Fig.3 presents the measured surface settlementSV_Ainduced by TA underH(Depth from the surface to the tunnel axis level)/D=2.0 and 5.0, respectively. The normal probability Gaussian curves proposed by Peck[3]were used to fit the measured data. The surface settlement of the 1st tunnel excavation has good agreement with O’Reilly and New[2], which is expected since TA is excavated in a greenfield site and this behavior is reected in the first tunnel settlement for all tests. Moreover, the Gaussian curves give a good fit whenVl=1.455% and 2.911%, then the goodness of the fit declines with the increase inVl, which coincides with the observations by Marshall et al.[5].

Fig.3 Gaussian curve fitting to the surface settlement induced by the TA under different H/D

As seen in Fig.4(a), the maximum surface settlementSmax_Alinearly increases withVl, which can also be seen in Shahin et al.[34]. From Fig.4(b), the soil volume loss of surface settlementVS_Ais smaller thanVlin all performed tests, especially at largeVland H which is in good agreement with Zheng et al.[35], who points out that the soil within the subsurface ground may exhibit an overall dilating response considering that the tests were conducted in a low-stress condition.

Fig.4 Variationsof Smax_A /D and VS_A with

3.1.2 Surface settlement due to excavation of the 2nd tunnel

The resultant surface settlementSVof different groups is plotted in Fig.5. Fundamentally, the distribution of the resultant ground settlement underH/D=2.0 and 5.0 changes from a “V” shape to a “W” shape step by step asSbecomes larger.

From Fig.5, it is clear that the position corresponding toSmax_Ais directly above TA during the tunnel excavation of TA. With the increase ofVlin TB, the position corresponding toSmax_Bgradually moves towards the axis of TB and the asymmetry of the settlement trough becomes more significant in T1, T2, T3 and T4 (S=1.5Dand 2.0D). But for the tests (T3 and T6) that have largerS, the position corresponding toSmax_Bis also just above TB, which means the excavation of TA has little influence on TB.

From Fig.6, it is clear that for T1, T2, T4 and T5, the corresponding location of the maximum surface settlementXmoves toward TB asVlincreases and the asymmetry of the settlement trough also becomes more significant. For T3, the corresponding locations of the maximum surface settlementXremains constant and the excavation of TA has little impact on TB. For T4, althoughXdoes not change, the settlement trough curves appear as an inflection point atX=1.5D.

Fig.5 Surface settlement of TA and TB for different ground volume

Fig.6 Variations in X/D with different

To further investigate the settlement caused by each excavation, the net surface settlementSV_Binduced by TB is shown in Fig.7. The settlement of TB is obtained from the resultant ground settlement subtracting the 1st tunnel settlement. Gaussian curves are again used to fit the experimental data. The goodness-of-fit of the Gaussian curves is shown to decrease with the development ofVlin the TB excavation, which is similar to the observations in the TA excavation.

Fig.7 Gaussian curve fitting to the surface settlement

Fig.8(a) shows theSmax_B/D-Vlcurves gained from the six tests. Basically, a non-linear relationship is found betweenSmax_BandVl·Smax_Bgrows up gradually asVldeveloped. Moreover, its magnitude is larger compared withSmax_Aas plotted in Fig.3, which is consistent with the conclusion obtained in clayey soils that the larger settlement in the 2nd tunnel excavation is caused by the interaction between the two tunnels[36-37].

Fig.8 Variations of Smax_B and Smax_B/ Smax_A with

To further illustrate the impact of parallel-tunnel interaction onSmax_B, variations inSmax_B/Smax_Awith differentVlare plotted in Fig.8(b). Basically,Sappears to be the most dominant factor influencing the values ofSmax_B/Smax_A. The influence of the twin-tunnel interaction is more significant in T1, T2, T4 and T5 (S=1.5Dand 2.5D), than in T3 and T6 (S=4.5D) as well as in the case of smallerH(H=2D).

Fig.9 presents the values of the empirical coefficient for surface settlementkunder differentVlfor differentH/D. Here,klandkrrepresent the empirical coefficients of the left and right sides of the settlement trough, respectively.kgradually increases withVlunder the sameS. Conversely, it decreases step by step with the increase ofS. Moreover,klgets closer tokrasSincreases, indicating that both sides of the settlement trough tend to be symmetrical.

Fig.9 Variations of k with different Vl for

3.2 Subsurface settlement

The resultant subsurface settlementSuof different groups is plotted in Fig.10. Basically, the distribution of Group 1 gradually changes from a “W” shape to a “V” shape asH0(Depth from the subsurface to the tunnel axis level)/Dbecomes larger. And the distribution of Group 2 remains in the shape of a “W”.From Fig.11, it is clear that for Group 1, the corresponding location of the maximum subsurface settlementXumoves toward TB asVlincreases. The asymmetry of the settlement trough for U1 and U2 becomes more significant, while for U3, the curves of the settlement trough undergo a process from asymmetry to symmetry and then back to asymmetry. As for Group 2,Xuis also just above TB and their settlement trough curves are quite similar, which means the excavation of TA has little influence on TB.

4 Summary and conclusions

Based upon the surface and subsurface settlements observed during the transparent soil model test, some useful conclusions are drawn as shown below:

1) With the increase of the ground volume loss, the Gaussian curve used to predict the ground settlement induced by the excavation of the two parallel tunnels demonstrates a decreasing trend.

2) The interaction of the parallel tunnels leads to greater maximum surface settlementSmax_Bduring the excavation of TB compared with that of TA. This effect weakens as the spacing between the parallel tunnels increases.

3) WhenS=1.5Dand 2.0D, the excavation of the 1st tunnel has a significant effect on the surface settlement of the 2nd tunnel, and the corresponding location ofSmaxgradually moves towards the axis of the 2nd tunnel with the increase ofVl. Moreover, the asymmetry of the settlement trough becomes more obvious. WhenS=4.5D, the excavation of the 1st tunnel has a marginal influence on the deformation of the 2nd tunnel.

Fig.10 Subsurface settlement of TA and TB for different ground volume

Fig.11 Variationsof Xu /D with different

4) Under the sameS,kgradually increases with the growth ofVlwhile it declines asSdevelops. The empirical coefficientskof the left and right sides get closer asSincreases.

Acknowledgements

The authors would like to acknowledge the financial support from the Chongqing Construction Science and Technology Plan Project (No. 2019-0045), Fundamental Research Funds for the Central Universities (No. 2019CDJDTM0007) and the Graduate Research and Innovation Foundation of Chongqing (Grant No. CYS18024).